Justification and head orientation effects

The grey-white interface is a convoluted three- dimensional contour, with a finite thickness. It will occupy a certain configuration of voxels in the MRI data, depending on both the biology of the real interface (its 'thickness' and anatomy) and the orientation of this interface in the scanner.

Orientation was not precisely fixed, though it was limited (see 3.10.1. and 3.10.2.). One might imagine that more voxels will be occupied by the same interface in certain orientations than in others.

Consider a small regular surface contour the size and shape of a single voxel (edge length 1 unit) in a space composed of identical voxels. The number of voxels that the surface contour even partly occupies is counted. Minimally, this surface could be orientated to occupy a single voxel of its containing space. On the other hand, it could be rotated and translated in three dimensions to intrude on 12 voxels. Thus, orientation alone could make a difference of 12-fold to the observed voxel count that would quantify this surface. Consider extending the surface contour so that whilst it remains cubical, its edge is now 1.1 units long. Minimally, this surface occupies (at least partly) 8 voxels in the original voxel space, whilst maximally it can still only intrude upon 12 . Thus the impact of orientation in voxel space on this slightly more "complex" (with regard to its embedding space) surface is reduced. If the surface in question is now made into a rectangular cuboid composed of two unit voxels with one common face, the ratio of maximum to minimum voxel occupation produced by orientation changes will be less than 12-fold, as all voxels even partly intruded upon by the common face of one voxel will already have been intruded upon by the other voxel through this common face. Thus, increasing complexity of the surface contour will reduce the effect of orientation of the contour in voxel space.

For surfaces which are any more complex, such thought experiments become very difficult, and the bias introduced by orientation (rotation and translation) can only be estimated empirically. For this reason, four individuals rescanned (two subjects twice each, two subjects three times) in different orientations, without attempting to align the brain to previous scanning positions, were studied. One of these

subjects was scanned lying in a tilted prone and two different supine positions, effecting radical alterations in imaging slice angle with respect to major brain axes. These scans were then segmented as usual and the relative intraindividual rotation in each case was estimated using the ratio M/L. The brains were assumed to be rigid bodies: for small changes in orientation, this is known to be effectively the case (Hajnal et al.,1995) .

For the six pairs of repeat segmentations, the minimum value of the ratio of the surface voxel counts for a given hemisphere was 0.947 for the right hemisphere and 0.948 for the left hemisphere. The intraclass correlation coefficient for all repetitions was 0.993. The full results, including the estimate of head rotation, M/L, are given in Appendix 5. The repeat segmentations were not included in the results.

Thus, even for radical changes in orientation (in the subject who was scanned supine and tilted prone), the change produced in the voxel count is small, and less than the volume variation produced by repeat segmentation of the same study alone (see section 3.7.). Empirically, therefore, for these four brains, it would appear that whilst orientation does have an effect on the voxel count, the complex nature of the SM surface with respect to the slices imaging it is such that this effect is small, and much smaller than the range of measured surface voxel counts across the entire subject group.

To extrapolate this finding to all the brains in the study would presuppose that all the brains are of equal complexity. Such assumptions may be the downfall of model- based, as opposed to stereological, design-based, derivations of structural parameters (Gundersen, 1986). Estimation of the complexity of the hemispheric SM surfaces for all the control subjects was performed in this report using three-dimensional fractal analysis of the SM surface (see next section) . This analysis shows that the complexity of the SM surfaces - in an

orientation, size and shape-independent analysis - of the normal subjects is in fact remarkably similar (see 4.1.7.). Therefore, the assumption that all the control SM surfaces are approximately of equal complexity is not unfounded. Thus the voxel counts obtained are not invalidated by the methodology used in their derivation; they are robust to the impact of orientation in the scanner. This applies also to all patients for whom the estimate of fractal dimension falls within the normal range. Patients with abnormal SM fractal dimension were not analysed with respect to surface areas: this was the case for 7/77 patients.

Stereological quantitation of surface areas is possible from parallel slices as revealed by Baddeley et al. (1986). Ideally, the elegant methodology propounded by these workers and employed already in the estimation of surface areas from postmortem data (Henery and Mayhew, 1989) would have been used. However, there are a number of restraints on data acquisition that prevents this methodology being used. Most importantly, the data was not collected with random (isotropic) orientation of imaging planes with respect to an arbitrary horizontal plane. Isotropic orientation is possible with current MRI technology (though not as yet for volumetric acquisitions); the plane of acquisition may be made isotropic random with respect to an arbitrary horizontal plane without the subject needing to be moved, and is indeed one of the great advantages of MRI. But all the scans were acquired for clinical analysis in the first instance, requiring that they were all as far as possible comparable, particularly with respect to neocortical structure and the hippocampus. Isotropic sectioning would greatly reduce the clinical value of scans analysed, almost invariably, by eye. For any large series of brains imaged for clinical reasons, visual analysis is likely to remain the favoured methodology for some time to come. Reformatting of the data is possible, but this will not create a new isotropic data set: the grey-white interface has already been demarcated and converted into voxels (under

clinical imperatives) and reformatting cannot now make it randomly acquired.

Gundersen (1986) states that biased, non-stereological analyses are hampered because experimenters need to deal with "only a vague idea about the significance of the bias which cannot be estimated in any non-trivial case". In this thesis, detailed analysis has allowed an attempt to estimate the bias of the method used here. It is small with respect to biological variability, presumably a result of the complexity and resultant isotropicity of the grey-white interface.

As discussed above, the exact numerical characteristics of the "real" grey-white interface cannot currently be analysed. All estimates will depend on part at least on the method used to derive those estimates - including visual assessment on macroscopic slices. The grey-white interface in our data is composed of a number of voxels: how these relate to the "real" interface cannot be determined, and will depend on the variables of biological interest - the anatomy of the interface and its thickness - and head orientation. The error that orientation may generate has been estimated and is small. Thus the voxel count is an estimate of the anatomy of the

"real" interface, and given its normal thickness in all except one case, more particularly a measure of the surface extent of the grey-white interface. In the one case with thickening of the grey-white interface on the images detected by an experienced neuroradiologist (case 6) , fractal dimension of the SM surfaces was abnormally low, so that surface area measures could not be performed in any case. The blurring of the grey-white interface did not have a significant effect on volume or block analysis (see section 3.4.2.)

3.13.2 Predicted and extra subcortical matter surface areas